there are 20 people in a room if they each shake eachothers hands once and only once. how many handshakes are there all together

Answer:

[tex]\boxed {\boxed {\sf 87 \ degrees}}[/tex]

Step-by-step explanation:

The angles in a triangle must add to 180 degrees.

We are given three angles: 2x+6, x, and 3x. Their sum must be 180, so we can create an equation.

[tex]2x+6+x+3x=180[/tex]

Combine like terms (all terms with an x) on the left side.

[tex](2x+x+3x)+6=180[/tex]

[tex]6x+6=180[/tex]

Now solve for x by isolating the variable.

6 is being added and the inverse of addition is subtraction. Subtract 6 from both sides.

[tex]6x+6-6=180-6\\6x=174\\[/tex]

x is being multiplied by 6. The inverse of multiplication is division. Divide both sides by 6.

[tex]6x/6=174/6 \\x=29[/tex]

Substitute 29 for x in the angle measures.

The largest angle is 87 degrees.

Answer:

2.575844

Step-by-step explanation:

This is a simple change of temp problem, from 539K to -62C but to start you have to change the C to K, which is simply adding 273 to the -62 so 211K.

Now you take P1/T1 = P2/T2 so,

6.58 = x

539 = 211

now cross multiply and divide, 211 x 6.58 then divide by 539.

this will give you your answer

***BTW DONT CLICK THE LINK ON THE ANSWER BELOW OR ABOVE THAT LEADS TO SOME MALWARE***

Answer: 18

Step-by-step explanation: hope it helps

Answer:

18

Step-by-step explanation:

two thirds of 27 is obv 18

2/5 , 1/2 , 7/10 , 10/7 , 3/1

Step-by-step explanation:

hope this helped

Answer:

1. Mean start of school year:

2. Median end of school year:

3. Range end of school year:

Answer:

45%

Step-by-step explanation:

45 out of 100 equals 45%.

Answer:

400 cm²

Step-by-step explanation:

25÷20 = 1.25

Area = 1.25 × 320

= 400 cm²

Answer:

500

Step-by-step explanation:

Base is 20, height is 16, the larger one is 1.25 times larger, so the height of the larger one is 16*1.25=20. This means that the area of the larger one is 20*25=500.

Answer:

Step-by-step explanation:

If the displacement of an object is proportional to the square of the time taken then the body is moving with uniformly accelerated motion as it will follow Newton's second equation of motion for a particular initial velocity

Answer:

$m + $12 = $26

Or

m + 12 = 26

Step-by-step explanation:

Amount spent by Richard = $m

Amount spent by Jordan = $12

Total amount spent together = $26

An equation that describes this situation would be:

$m + $12 = $26

Or

m + 12 = 26

Answer:

a 6 - 3x , hope I helped. have a nice day

Answer:

3 grey and 1 red

Step-by-step explanation:

5 x 3 = 15

15 + 7 = 22

Answer:

280 6th graders

Step-by-step explanation:

65%=0.65

x=total students

0.65x=182

x=182/0.65

x=280

Answer:

C

Step-by-step explanation:

Answer:

36.5miles/gallon

Step-by-step explanation:

Given the equation y=36.5x which represents the number of miles, y, that Katherine can drive her car for every, x, gallons of gas. The rate of change of the function is expressed as dy/dx

On differentiating the function;

dy/dx = 36.5

Hence the rate of change of the function is 36.5miles/gallon

Answer:

1,420 grams per 100 baseballs

Step-by-step explanation:

Set up an equation:

Variable x = grams per 100 baseballs

1/14.2 = 100/x

Cross multiply

1 × x = 14.2 × 100

1x = 1420

x = 1420

Answer:

65%

Step-by-step explanation:

52 × 100 ÷ 80 = 65% from club members

Answer:

inside the circle

Step-by-step explanation:

Khan Academy

Answer:

iwillanswer

Genius

4.3K answers

14.6M people helped

17 one point shots and 39 two point shots were made

Solution:

Given that,

At a basketball​ game, a team made 56 successful shots

They were a combination of​ 1- and​ 2-point shots

Let "x" be the number of 1 point shots

Then, 56 - x is the number of two point shots

The team scored 95 points in all

Therefore,

1(number of 1 point shots) + 2(number of two point shots) = 95

x + 2(56 - x) = 95

x + 112 - 2x = 95

x = 112 - 95

x = 17

Then, number of two point shots = 56 - x = 56 - 17 = 39

Thus 17 one point shots and 39 two point shots were made

Given:

The figure of a right triangle.

To find:

All the six trigonometric ratios for the angle θ.

Solution:

Using the Pythagoras theorem, we get

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

[tex]Hypotenuse^2=(9)^2+(12)^2[/tex]

[tex]Hypotenuse^2=81+144[/tex]

[tex]Hypotenuse^2=225[/tex]

Taking square root on both sides, we get

[tex]Hypotenuse=15[/tex]

Now, the six trigonometric ratios for the angle θ are:

[tex]\sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\sin\theta=\dfrac{12}{15}[/tex]

[tex]\sin\theta=\dfrac{4}{5}[/tex]

[tex]\cos\theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]\cos\theta=\dfrac{9}{15}[/tex]

[tex]\cos\theta=\dfrac{3}{5}[/tex]

[tex]\tan\theta=\dfrac{Perpendicular}{base}[/tex]

[tex]\tan\theta=\dfrac{12}{9}[/tex]

[tex]\tan\theta=\dfrac{4}{3}[/tex]

[tex]\csc\theta=\dfrac{1}{\sin \theta}[/tex]

[tex]\csc\theta=\dfrac{1}{\dfrac{4}{5}}[/tex]

[tex]\csc\theta=\dfrac{5}{4}[/tex]

[tex]\sec\theta=\dfrac{1}{\cos \theta}[/tex]

[tex]\sec\theta=\dfrac{1}{\dfrac{3}{5}}[/tex]

[tex]\sec\theta=\dfrac{5}{3}[/tex]

[tex]\cot\theta=\dfrac{1}{\tan \theta}[/tex]

[tex]\cot\theta=\dfrac{1}{\dfrac{4}{3}}[/tex]

[tex]\cot\theta=\dfrac{3}{4}[/tex]

Therefore, the six trigonometric ratios are [tex]\sin\theta=\dfrac{4}{5},\cos\theta=\dfrac{3}{5},\tan\theta=\dfrac{4}{3},\csc\theta=\dfrac{5}{4},\sec\theta=\dfrac{5}{3},\cot\theta=\dfrac{3}{4}[/tex].

Answer:

x=12 y=3

Step-by-step explanation:

Since the scale factor is 1:3, that means that the length and width of Q multiplied by 3 gives the corresponding length and width of P.

Similarly, the length and width of P divided by 3 gives the corresponding length and width of Q.

With this, 9/3=3, which is the value of y.

4*3=12, which is the value of x.

===================================================

Explanation:

We could add 9 to both sides, and then apply the square root to both sides. Don't forget about the plus minus

x^2 - 9 = 0

x^2 = 9

x = sqrt(9) or x = -sqrt(9)

x = 3 or x = -3

To check these answers, you replace x with those values we found. I'll show you how to check x = 3

x^2 - 9 = 0

(3)^2 - 9 = 0

9 - 9 = 0

0 = 0

So that confirms x = 3. The confirmation for x = -3 is nearly the same. Keep in mind that (-3)^2 = (-3)(-3) = 9. You'll be squaring the negative as well.

------------------

Another method you could do is to use the difference of squares rule

x^2 - 9 = 0

x^2 - 3^2 = 0

(x - 3)(x + 3) = 0

Now apply the zero product property. This effectively means you set each factor equal to zero and solve for x

x-3 = 0 or x+3 = 0

x = 3 or x = -3

We end up with the same solution set.

Yet another method you could use is the quadratic formula, but that may be overkill. It's still good practice to do.

Graphing is a visual way to find the answers. You'll graph y = x^2 - 9 and look to see where the curve crosses or touches the horizontal x axis.

Answer:

S₁₅ = 645

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Using the nth term formula [tex]a_{n}[/tex] = 5n + 3 , then

a₁ = 5(1) + 3 = 5 + 3 = 8

a₂ = 5(2) + 3 = 10 + 3 = 13 , then

d = a₂ - a₁ = 13 - 8 = 5

Thus

S₁₅ = [tex]\frac{15}{2}[/tex] [ (2 × 8) + (14 × 5) ]

     = 7.5( 16 + 70)

     = 7.5 × 86

     = 645

x = 36

Step-by-step explanation:

The angles 4x and x are supplementary, meaning they add up to 180; therefore we have

[tex]4x + x = 180[/tex]

[tex]5x = 180[/tex]

dividing both sides by 5 gives

[tex]x = 36[/tex]

the measure of angle x is 36 and that of 4x is 4 * 36 = 144

The angle opposite to 4x also measures 144 and the one opposite to x is 36.

Answer:

x° + 4x° = 180°

5x° = 180°

x° = 180°/5

x° = 36°

The rate of change is the slope. The slope is the number in front of the x

Function 1 rate of change is -1/2

Function 2 rate of change is -3/4

The greater rate of change would be the steepest slope.

Function 2 has the greater rate of change

See the attached picture.

Answer:

puede cargar 205 killos pero no mas de 260 por el peso.

Step-by-step explanation:

5t. 3q 85kg

Answer:

Step-by-step explanation:

23+87+98=208

2.08+1=3.08

3.08-----> 308p